Efficient parameter identification using nonsmooth and nonconvex regularization for inverse problem of diffuse optical tomography
Abstract To better reconstruct the piecewise constant optical coefficients in diffuse optical tomography, nonconvex and nonsmooth approximation of weak Mumford–Shah functional is considered in this paper. We theoretically analyze the existence of minimizers in piecewise constant finite element space...
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Nature Portfolio
2025-07-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-025-07560-y |
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| author | Jinping Tang Bo Bi |
| author_facet | Jinping Tang Bo Bi |
| author_sort | Jinping Tang |
| collection | DOAJ |
| description | Abstract To better reconstruct the piecewise constant optical coefficients in diffuse optical tomography, nonconvex and nonsmooth approximation of weak Mumford–Shah functional is considered in this paper. We theoretically analyze the existence of minimizers in piecewise constant finite element space and constrained finite dimensional subsets. However, optimizing such minimization problems presents a computational challenge due to the nonconvex and non-differentiable properties. To overcome these difficulties, we propose a fast graduated nonconvex alternative directional multiplier method to solve this numerical problem. Compared with graduated nonconvex Gaussian–Newton, $$TV^q$$ Gaussian–Newton, and TV Gaussian–Newton, our simulations show that the proposed GNC-ADMM can well keep edges and values of the anomaly with fewer iteration steps and fewer measurements. |
| format | Article |
| id | doaj-art-660842e80b7840368df44867a830d450 |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-660842e80b7840368df44867a830d4502025-08-20T04:02:45ZengNature PortfolioScientific Reports2045-23222025-07-0115111210.1038/s41598-025-07560-yEfficient parameter identification using nonsmooth and nonconvex regularization for inverse problem of diffuse optical tomographyJinping Tang0Bo Bi1School of Computer and Big data (School of Cyber and Security), Heilongjiang UniversitySchool of Public Health, Hainan Medical University (Hainan Academy of Medical Sciences)Abstract To better reconstruct the piecewise constant optical coefficients in diffuse optical tomography, nonconvex and nonsmooth approximation of weak Mumford–Shah functional is considered in this paper. We theoretically analyze the existence of minimizers in piecewise constant finite element space and constrained finite dimensional subsets. However, optimizing such minimization problems presents a computational challenge due to the nonconvex and non-differentiable properties. To overcome these difficulties, we propose a fast graduated nonconvex alternative directional multiplier method to solve this numerical problem. Compared with graduated nonconvex Gaussian–Newton, $$TV^q$$ Gaussian–Newton, and TV Gaussian–Newton, our simulations show that the proposed GNC-ADMM can well keep edges and values of the anomaly with fewer iteration steps and fewer measurements.https://doi.org/10.1038/s41598-025-07560-y |
| spellingShingle | Jinping Tang Bo Bi Efficient parameter identification using nonsmooth and nonconvex regularization for inverse problem of diffuse optical tomography Scientific Reports |
| title | Efficient parameter identification using nonsmooth and nonconvex regularization for inverse problem of diffuse optical tomography |
| title_full | Efficient parameter identification using nonsmooth and nonconvex regularization for inverse problem of diffuse optical tomography |
| title_fullStr | Efficient parameter identification using nonsmooth and nonconvex regularization for inverse problem of diffuse optical tomography |
| title_full_unstemmed | Efficient parameter identification using nonsmooth and nonconvex regularization for inverse problem of diffuse optical tomography |
| title_short | Efficient parameter identification using nonsmooth and nonconvex regularization for inverse problem of diffuse optical tomography |
| title_sort | efficient parameter identification using nonsmooth and nonconvex regularization for inverse problem of diffuse optical tomography |
| url | https://doi.org/10.1038/s41598-025-07560-y |
| work_keys_str_mv | AT jinpingtang efficientparameteridentificationusingnonsmoothandnonconvexregularizationforinverseproblemofdiffuseopticaltomography AT bobi efficientparameteridentificationusingnonsmoothandnonconvexregularizationforinverseproblemofdiffuseopticaltomography |